Question

If vectors \(5\hat i-\lambda\hat j+2\hat k\) and \(2\hat i+3\hat j+4\hat k\) are perpendicular to each other, then the value of \(\lambda\) is:

• A. 3
• B. 4
• C. 6
• D. 0

Hint:

Set the dot product of the two vectors to zero and solve for \(\lambda\).

Answer 1

The Correct Option is C

Step 1: Use the perpendicularity condition:
Two vectors are perpendicular exactly when their dot product is \(0\).

Step 2: Compute the dot product:
\[ (5)(2)+(-\lambda)(3)+(2)(4)=10-3\lambda+8=18-3\lambda \]

Step 3: Solve for \(\lambda\):
\[ 18-3\lambda=0 \implies \lambda=6 \]

Final Answer:
\[ \boxed{\lambda=6} \]